Space of modular forms of level 495, weight 2, and Character 495.bs

• Label: 495.2.bs
• Level: $495$
• Weight: $2$
• Character orbit: 495.bs
• Rep. character: $\chi_{495}(7,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1088$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bs (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

	Total	New	Old
Modular forms	1216	1216	0
Cusp forms	1088	1088	0
Eisenstein series	128	128	0

Trace form

\( 1088 q - 10 q^{2} - 14 q^{3} - 6 q^{5} - 40 q^{6} - 10 q^{7} - 40 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.2.bs.a	$495$	$2$	495.bs	495.as	$60$	$1088$	$68$	$3.953$		None		$8$	$0$	\(-10\)	\(-14\)	\(-6\)	\(-10\)		$\mathrm{SU}(2)[C_{60}]$